Pictures of social media appeared to show Ward-Prowse's bone sticking out of his leg after a challenge with Ryan Sessegnon.
But Hasenhuttl says the injury is only a deep gash on his knee.
"I'm happy that Prowsey's injury is not that bad," he said. "That would've been horrible – to lose the game and lose him for longer, so this is the positive thing.
"It's only a cut on the knee – a deep one and you could see the bone, so it will take a little bit of time to heal, but if it was a ligament injury, it would be more of a problem for us."